Apparatus and methods for making azimuthal resistivity measurements

ABSTRACT

A resistivity measuring tool used in a drillstring having a drill bit on a distal end for drilling a wellbore in a formation includes a tool body having a longitudinal axis, a sensor configured to measure the angular position of the tool body relative to the wellbore, at least one axial antenna including a wire winding for generating an axial magnetic moment parallel with the longitudinal axis, and at least one transverse antenna. The transverse antenna includes an antenna body disposed within a pocket extending radially inward from an outer surface of the tool body and one or more turns of wire wound around the antenna body, the wire winding generating a transverse magnetic moment orthogonal to the longitudinal axis.

CROSS-REFERENCE TO RELATED APPLICATIONS

This divisional application claims priority to U.S. Ser. No. 14/303,232,filed Jun. 12, 2014 and allowed Nov. 23, 2015, and claims benefit ofU.S. Provisional Application No. 61/834,272 filed Jun. 12, 2013, whichare both incorporated herein by reference in their entirety.

FIELD

Embodiments disclosed herein relate to, for example, apparatus andmethods for making azimuthal electromagnetic resistivity measurements.

BACKGROUND AND SUMMARY

Well logging, also known as borehole logging, is the practice of makinga detailed record (a well log) of the geologic formations penetrated bya borehole. Resistivity logging is a method of well logging that worksby characterizing the rock or sediment in a borehole by measuring itselectrical resistivity. Resistivity is a fundamental material propertywhich represents how strongly a material opposes the flow of electriccurrent. Most rock materials are essentially insulators, while theirenclosed fluids are conductors. Hydrocarbon fluids are an exception,because they are almost infinitely resistive. When a formation is porousand contains salty water, the overall resistivity will be low. When theformation contains hydrocarbons, or contains very low porosity, itsresistivity will be high. High resistivity values may indicate ahydrocarbon bearing formation.

In one aspect, embodiments disclosed herein relate to a resistivitymeasuring tool used in a drillstring having a drill bit on a distal endfor drilling a wellbore in a formation including a tool body having alongitudinal axis, a sensor configured to measure the angular positionof the tool body relative to the wellbore, at least one axial antennaincluding a wire winding for generating an axial magnetic momentparallel with the longitudinal axis, and at least one transverseantenna. The transverse antenna includes an antenna body disposed withina pocket extending radially inward from an outer surface of the toolbody and one or more turns of wire wound around the antenna body, thewire winding generating a transverse magnetic moment orthogonal to thelongitudinal axis. At least one antenna is configured to transmitelectromagnetic energy into the formation and induce a voltage signalrelated to a parameter of the formation in a different antenna.

In other aspects, embodiments disclosed herein relate to a method ofmaking resistivity measurements of a formation from a wellbore beingdrilled including providing a resistivity measuring tool including atool body having a sensor configured to measure the angular position ofthe tool body relative to the wellbore, at least one axial antennaincluding a wire winding for generating an axial magnetic moment, and atleast one transverse antenna disposed proximate to an outer surface ofthe tool body and including a wire winding for generating a transversemagnetic moment. The method further includes transmittingelectromagnetic energy into the formation from at least one of theantennas, thereby inducing a voltage signal related to a formationparameter in the wire winding of a non-transmitting antenna, measuringan angular position of the tool body relative to the wellbore with thesensor, and correlating the formation parameter with the measuredangular position of the tool body.

In yet other aspects, embodiments disclosed herein relate to a method ofmaking resistivity measurements of a formation from a wellbore beingdrilled including providing a resistivity measuring tool including atool body having a sensor configured to measure the angular position ofthe tool body relative to the wellbore, at least two axial antennas eachincluding a wire winding for generating an axial magnetic moment, and atransverse antenna disposed between the two axial antennas and includinga wire winding for generating a transverse magnetic moment. The methodfurther includes substantially simultaneously driving a current to thewire windings of the two axial antennas for generating a current loop inthe formation, thereby inducing a voltage signal related to a formationparameter in the wire winding of the transverse antenna disposedtherebetween, measuring an angular position of the tool body relative tothe wellbore with the sensor, and correlating the formation parameterwith the measured angular position of the tool body.

In still other aspects, embodiments disclosed herein relate to a methodof data binning including partitioning a circumference of a tool faceinto M number of sectors, defining each data point relating toresistivity information by a fidelity function g(Φ), assigning to eachdata point a weight for each of the M number of sectors, wherein theweight is associated with an integral of the fidelity function g(Φ) overthe sector, and computing an average of the data points weighted bytheir respective weights for each of the M sectors.

BRIEF DESCRIPTION OF THE FIGURES

FIGS. 1A-C illustrate embodiments of an azimuthal resistivitymeasurement tool having a transverse elemental antenna.

FIGS. 2A-B illustrate embodiments of an azimuthal resistivitymeasurement tool having multiple azimuthally-spaced transverse elementalantennas.

FIG. 3 illustrates an embodiment of transverse elemental antennacomponents.

FIGS. 4A-D illustrate embodiments of composite transverse antennaconfigurations.

FIG. 5 illustrates an embodiment of axial antenna components.

FIGS. 6A-C illustrate embodiments of co-located antennas.

FIG. 7 illustrates a graph showing measured signal responses due to ananisotropic formation with and without measurement compensation.

FIG. 8 illustrates a graph showing measured signal responses due to ananisotropic formation with and without measurement compensation.

FIG. 9 illustrates a fidelity function related to an embodiment of databinning methods.

FIG. 10 illustrates a flowchart showing an embodiment of a data binningmethod.

DETAILED DESCRIPTION

A downhole resistivity measuring tool suitable for use in any downholeenvironment is disclosed. A drill bit is secured to the lower end of thedrill collar measurement tubular for drilling a rock formation. Themeasurement tubular may also include a resistivity measuring tool,communications package, and other downhole measurement tools to measure,for example, the acoustic velocity, the natural radiation, and thedensity of the formation surrounding the wellbore. The resistivitymeasuring tool disclosed may be used both when the measurement tubularis rotating, slowly rotating, or not rotating. The communicationspackage communicates between the electromagnetic resistivity tool andother downhole measurement tools and a surface control system by anymeans. For example, the communications package may use mud pulsetelemetry and electrical telemetry techniques for communicating with asurface control system. The measurement tool includes a sensorconfigured to measure the angular position of the tool body relative tothe wellbore.

Resistivity measuring tools use an electric coil to generate analternating current loop in the formation by induction. The alternatingcurrent loop, in turn, induces a voltage signal in a receiving coillocated elsewhere in the tool. The voltage signal induced in thereceiving coil is related to a parameter of the formation. Multipletransmitting and receiving coils may be used to focus formation currentloops both radially (depth of investigation) and axially (verticalresolution).

As used herein in reference to antennas, “transverse” refers to amagnetic moment, created by electrical current in a wire loop, having adirection orthogonal or substantially orthogonal relative to alongitudinal axis of the tool body. “Axial” refers to a magnetic moment,created by electrical current in a wire loop, having a direction alignedor substantially aligned or parallel with a longitudinal axis of thetool body.

For frame of reference and as used herein, the Z-axis points along alongitudinal axis of the tool body. The X-axis falls in a gravity planecontaining the Z-axis. In a tool including transmitter and receiverantennas oriented in the X, Y, or Z directions, nine differentcombinations of transmitter and receiver antennas are possible: XX, XY,XZ, YX, YY, YZ, ZX, ZY, and ZZ, where the first letter indicates theorientation of the transmitter antenna and the second letter theorientation of the receiver antenna. Those combinations provide means toimage the formation around a borehole. In particular, the XZ, ZX, YZ,and ZY components or their combinations provide the most usefulazimuthal resistivity measurement for resolving an adjacent boundary orother geological features around a wellbore.

FIGS. 1A-C illustrate embodiments of a resistivity measuring tool 100including a transverse receiving antenna 120 and an axial transmittingantenna 110. The axial transmitting antenna 110 may be placed in eitherthe uphole direction or the downhole direction relative to thetransverse receiving antenna 120. The receiving antenna 120 is spacedapart from the transmitting antenna 110 at a predefined distance. Thedirection of the magnetic moment of the axial transmitting antenna 110remains substantially unchanged as the measurement tool 100 rotates,whereas that of the transverse receiving antenna 120 rotates with thetool 100. To make an azimuthal measurement, a current (e.g.,alternating) is driven to the axial transmitting antenna 110 (also knownas firing the antenna) at moments controlled by a microcontroller (notshown) of the tool to transmit electromagnetic waves into thesurrounding medium at a selected frequency. The transmitted signal, whenencountering a resistivity boundary near the borehole, is reflected backand received by the transverse receiving antenna 120. The detectedvoltage signal is recorded at one or more tool face angles as the toolrotates. The measurement tool includes a sensor 102 configured tomeasure the angular position of the tool body relative to the wellbore(e.g., tool face angles). For example, the sensor 102 may be anaccelerometer, a magnetometer, a gyro, or any other known sensor orsensor combination. If multiple transverse receiving antennas are used,the reflected electromagnetic wave may be detected simultaneously by thereceiving antennas.

FIGS. 1B and 1C illustrate embodiments of a resistivity measuring tool100 including a transverse receiving antenna 120 and a pair ofsymmetrical (FIG. 1B) or asymmetrical (FIG. 1C) axial transmittingantennas 110. The pair of axial transmitting antennas 110 may beenergized sequentially or simultaneously as explained later. And asfurther discussed below, by combining and processing the signals due tothe two axial transmitting antennas, whether fired sequentially orsimultaneously, a formation resistivity anisotropy effect on theazimuthal measurement may be reduced or removed, leaving the processedresponse largely sensitive to an adjacent bed boundary. Alternatively,the signals generated by the two axial transmitting antennas 110 may beprocessed to remove or reduce the bed boundary effect and enhance theformation resistivity anisotropy effect.

FIGS. 2A and 2B illustrate an embodiment of a resistivity measuring tool100. Multiple transverse receiving antennas 120 are located around acircumference of the tool body 105 and separated by varying angles inthe azimuthal direction, preferably 90 degrees in the azimuthaldirection, although a different separation angle may also be used. Forexample, in certain embodiments, two transverse antennas may beseparated by at least about 30 degrees, at least about 45 degrees, or atleast about 60 degrees. Transverse receiving antennas are preferablylocated at substantially the same longitudinal position (e.g., along theZ-axis) on the tool axis but may be located at different longitudinalpositions as well. One or more axial transmitting antennas 110 arepreferably placed longitudinally on opposite sides of the receivingantenna(s) 120, although they may also be placed on the same side of thereceiving antenna(s) 120. When more than one axial transmitting antennas110 are used, they may be fired sequentially or simultaneously. Themeasured signals due to the two transmitting antennas 110 may beprocessed to either remove or enhance the formation resistivityanisotropy effect, discussed in greater detail below. The resistivitymeasuring tool having multiple transverse receiving antennasazimuthally-spaced around the tool body may be more preferably used tomeasure formation resistivity when the tool is slowly rotating or notrotating.

FIG. 3 illustrates an embodiment of transverse antenna components. Anantenna pocket 122 is formed (e.g., machined, molded, etc.) near anouter surface of a drill collar body 105. The pocket 122 extendsradially inward from the outer surface of the drill collar body to amaximum radial depth of one half a diameter of the tool body.Preferably, the pocket may be at least 0.25 inches deep, or up to 0.5inches deep, or up to about one inch deep, or deeper. The pocket 122 maybe any shape including square, rectangle, circle, ellipse or othershapes. In the case of a square or rectangle pocket, the corners of thepocket may be smoothed to reduce stress accumulation around the corners.An antenna body 124 is configured to substantially correspond in shapewith and to fit within the pocket 122. The antenna body 124 may be madeof any non-conducting material, including but not limited to as PEEK,fiberglass, or ceramic. An antenna wire 126 is wound around the antennabody 124 such that the wire 126 extends substantially along thelongitudinal direction (Z-axis) of the tool axis 101. One or multipleturns of wire may be wound around the antenna body 124. To help hold thewire in place, wire grooves 125 may be formed on the outer surface ofthe antenna body 124. The wire 126 may be insulated with Teflon or othernon-conducting material to prevent short-circuiting between turns andfrom being exposed to drilling fluids. The antenna body 126 with thewound antenna wire 125 is inserted into the antenna pocket 122 such thatthe moment of the antenna points in a transversal direction. The ends ofthe antenna wire 125 exit the antenna pocket 122 to a nearby pocket (notshown) formed in the collar body 105 where a preamplifier may be placedto amplify the received signal before the signal is fed to an electronicboard (not shown).

An antenna shield 128 may be placed over the antenna body 124 after itis inserted within the antenna pocket 122. Preferably, the antennashield is configured to sit flush with an outer surface of the collarbody 105. The antenna shield 128 may be made of the same material as thecollar body 105, or a different, preferably harder, material. In oneembodiment, the antenna shield and collar body may be made of stellite.One or more openings 130 may be formed in the antenna shield 128 toallow electromagnetic energy to pass through. The openings 130 arepreferably aligned in the azimuthal direction. The antenna shield 128may be attached to the collar body 105 either with bolts or by weldingor other means.

Non-conducting, abrasion-resistant materials, or potting material, maybe used to fill any remaining voids or cavities within the antennapocket 122, after the antenna body 124 is inserted and the antennashield 128 is attached, for further protection of the antenna wire 126.To increase the antenna efficiency, the potting material may be mixedwith magnetic materials so that the mixture has a relative magneticpermeability greater than 1. Such a transversal antenna may be referredto as an “elemental” transverse antenna. Because the shield openingsextend substantially along the circumferential direction, they may besubject to wear and tear during drilling. To help protect the pottingmaterial from being damaged or worn out, the shield openings may benarrow. To further protect the potting material, curved openings may beused instead of straight openings. Each curved opening is preferablysymmetric with respect to the center point of the opening.

FIGS. 4A-D illustrate cross-section views of a collar body 105 having apair of transverse elemental antennas 120 combined to form a compositetransverse antenna. Any number of composite transverse antennaconfigurations may be formed. FIG. 4A illustrates an antenna body 124and antenna wire winding 126 within a pocket 122 and covered by anantenna shield 128, forming a transverse elemental antenna 120. Current“I” flows in the antenna wire winding 126 in a direction shown by thearrows to generate a transverse magnetic moment M_(T) substantiallyorthogonal to the tool body axis. FIG. 4B illustrates a pair oftransverse elemental antennas 120 disposed opposite each other on thecollar body 105 and connected to form a composite transverse antenna.The transverse elemental antennas 120 may be connected by a wire 121 ofany diameter that extends from one transverse antenna to the other. Theconnecting wire 121 may be disposed within the collar body 105 fordamage protection, for example, extending through a drilled hole in thecollar body 105 starting from one transverse elemental antenna 120 andending at the second transverse elemental antenna 120. Alternatively, agroove may be machined on an outer surface of the collar body 105, thewire 121 disposed within the groove running between the two transverseantennas, and the groove welded for mechanical protection. Yet othermeans of wire connection between two transverse elemental antennas arepossible. For instance, the wire from each transverse elemental antennamay exit directly to an adjacent electronics board for signalcommunication. In this case, the pair of transverse elemental antennasmay be connected indirectly through the electronics board. The pair oftransverse elemental antennas 120 may be connected or coupled indifferent ways to generate different combinations of transverse magneticmoments.

FIG. 4B illustrates transverse elemental antennas 120, with currents Iflowing in the antenna wire windings 126 in directions shown by thearrows, which generate transverse magnetic moments M_(T) in the sametransverse direction. In this configuration, the transverse antennamoments M_(T) may be additive to each other and the pair of transverseantennas 120 produce a composite transversal antenna with its effectivecenter on the tool axis. That is, the pair of elemental antennas shownin FIG. 4B are connected in series so that signals from each are addedto form a stronger signal (e.g., a composite transverse moment=2M_(T)).

FIG. 4C illustrates transverse elemental antennas 120, with currents Iflowing in the antenna wire windings 126 in direction shown by thearrows, which generate transverse magnetic moments M_(T) in oppositetransverse directions. A composite transverse antenna in thisconfiguration will not produce any significant transverse magneticmoment component (e.g., a composite transverse moment≈0). Rather, theresulting magnetic moments may resemble a quadrupole. An electricalcurrent flowing in the tool's longitudinal direction will produce amagnetic field circulating around the collar. The magnetic fields on theopposite sides of the collar will point to opposite azimuthal directionswhen viewed in a Cartesian coordinate system, which will produce aresponse in the quadrupole antenna.

FIG. 4D illustrates transverse elemental antennas 120, with currents Iflowing in the antenna wire windings 126 in directions shown by thearrows, which generate transverse magnetic moments M_(T) in the sametransverse direction, similar to FIG. 4B. However, the antennas shown inFIG. 4D are electrically connected in parallel. Therefore, transversemagnetic moments M_(T) are not added (e.g., a composite transversemoment=M_(T)), however if one antenna fails the other still provides thesame signal strength. That is, transverse elemental antennaselectrically connected in parallel provide redundancy in case oneantenna fails, the composite antenna will still have the same moment asif there was no failure.

FIG. 5 illustrates an embodiment of axial antenna components. An antennagroove 112 may be formed in an outer surface of the tool body 105. Thewidth of the antenna groove 112 may be at least one-half inch or up toeight inches or greater, but preferably between one inch and six inchesmeasured along the longitudinal direction of the collar. A depth of theantenna groove 112 may be at least 0.05 inches, at least 0.1 inches, atleast 0.25 inches, at least 0.5 inches, at least one inch, or greater. Awire groove 114 may be formed in an outer surface and near the center ofthe antenna groove 112. The wire groove 114 should be wide and deepenough to hold one or multiple turns of antenna wire 115. Individualwire ways may also be created to hold each turn of wire in place.Longitudinal slots 116 may be formed in an outer surface of the antennagroove 112 for passage of electromagnetic wave energy, and may bereferred to as passage slots. The passage slots 116 may be at least 0.25inches deep, or at least 0.5 inches deep, or at least one inch deep,depending on the size of the collar. The passage slots 116 may beseparated from each other by at least approximately 0.25 inches, or atleast 0.5 inches, or at least one inch, or at least two inches, orgreater. One or multiple turns of antenna wire 115 may be disposed inthe wire groove 114. The antenna wire 115 may exit the antenna groovethrough pressure sealed connectors to a pressure-sealed pocket (notshown) near the antenna groove 112.

An antenna shield 118 may be placed on top of the antenna groove 112 tocover the antenna wire. The antenna shield 118 may be made of the samematerial as the collar body 105 or a different, preferably harder,material (e.g., stellite) to protect the antenna wire from being damagedduring drilling. The antenna shield 118 may include two or morecylindrical pieces, each having multiple slots 119 formed within. Theshield slots 119 may be aligned with the passage slots 116 formed in theantenna groove 112. The shield slots 119 may be at least 0.05 incheswide, or at least 0.1 inches wide, or at least 0.5 inches wide, or atleast one inch wide, but are preferably within 0.1 to 0.5 inches wideand do not have to be the same width as the underneath passage slots.The thickness of the shield may be at least 0.05 inches, or at least 0.1inch, or at least 0.25 inches, or at least 0.5 inches, or at least oneinch, or greater. The shield 118 may be secured or locked to the collarbody 105 either through welding or by bolts. Further, the antenna bodymay be vacuumed and potted with non-conducting material for integrityand damage protection. The surface of the antenna may be polished toremove any outstanding material.

FIGS. 6A-C illustrate embodiments of co-located antennas in the drillcollar body. FIG. 6A illustrates an embodiment of co-located transverseantennas, each including a pair of transverse elemental antennas 120connected as discussed in reference to FIGS. 4A-D. The pairs oftransverse antennas generate magnetic moments M_(T) in the samedirection, although any of the composite transverse antenna arrangementsmay be configured. Connecting wires 121 and wire ways between the pairsof transverse elemental antennas 120 preferably do not intercept, andeach transverse elemental antenna 120 transmits or receiveselectromagnetic energy independently. FIG. 6B illustrates an embodimentof co-located transverse elemental antennas 120 and axial antennas 110.The pair of transverse antennas 120 generate magnetic moments M_(T) inthe same direction, although any of the composite transverse antennaarrangements may be configured. The pair of axial antennas 110 generatemagnetic moments M_(A) in either direction. The axial antenna 110includes two axial elemental antennas spaced apart by 180 degrees in theazimuthal direction and connected by a wire way for wire passage 121.The wire ways preferably do not intercept each other. In certaininstances, the axial antenna may include a single axial antenna, inwhich case no wire way will be needed.

Various methods of making azimuthal resistivity measurements with andwithout tool rotation are disclosed. One purpose of azimuthalresistivity measurements is generating information for resolution of theazimuthal direction of and distance to an adjacent boundary near thewellbore. This may be accomplished with one axial transmitting antennaand one elemental transversal receiving antenna. While the transmittingantenna is firing, a signal is acquired from the receiving antenna asthe tool rotates. In the presence of a bed boundary near the wellboreand assuming that the boundary is azimuthally located at a tool faceangle of φ₀, the signal measured will vary with tool face angle as:

A(φ)=A ₀ cos(φ+φ₀)  (1)

where A₀ is the maximum (in the absolute value) value of the azimuthalsignal when the transversal receiver antenna points toward the boundary,i.e., at the tool face angle φ₀ and φ is tool face angle. In equation(1), A₀ depends on the resistivities of both the near and the remotebeds, distance to the boundary, coil spacing, frequency, antennamoments, and the driving current in the transmitting antenna. Solvingequation (1) for A₀ and φ₀ requires at least two independentmeasurements, which may be accomplished by taking measurements at two ormore distinct tool face angles. It may be expressed as:

A ₁ =A ₀ cos(φ₁+φ₀)+e ₁  (2)

A ₂ =A ₀ cos(φ₂+φ₀)+e ₂  (3)

A _(n) =A ₀ cos(φ_(n)+φ₀)+e _(n)  (4)

In equations (2)-(4), e₁, e₂, . . . e_(n) are measurement errors, andthe equations may be solved in the least-square sense which is wellknown.

In the case where the tool does not rotate, multiple transverse antennasare used to generate independent measurements at different tool faceangles. For example, two transverse elemental antennas separated by 90degrees in the azimuthal direction, may be used. They are preferablylocated at the same longitudinal position on the tool axis but this isnot necessary. Measurements from each antenna may be written as:

A ₁ =A ₀ cos(φ₁+φ₀)+e ₁  (5)

A ₂ =A ₀ cos(φ₁+90+φ₀)+e ₂ =A ₀ sin(φ₁+φ₀)+e ₂  (6)

Equations (5)-(6) may be solved for A₀ and φ₀ using a least squaresmethods. Here, in a cross-section view, the magnetic moments generatedby the two transversal antennas are assumed to be orthogonal to eachother, although not necessary. In general, the two transverse elementalantennas may be separated in the azimuthal direction by any anglebetween 0° and 360°. In this case, equations (5)-(6) becomes:

A ₁ =A ₀ cos(φ₁+φ₀)+e ₁  (7)

A ₂ =A ₀ cos(φ₁+Δφ+φ₀)+e ₂  (8)

where Δφ is the azimuthal angle separation between the two antennas.

For the special case of equations (5)-(6) and in the absence ofmeasurement noises, both A₀ and φ₀ may be computed as:

$\begin{matrix}{A_{0} = \left( {A_{1}^{2} + A_{2}^{2}} \right)^{1/2}} & (9) \\{\varphi_{0} = {\tan^{- 1}\left( \frac{A_{2}}{A_{1}} \right)}} & (10)\end{matrix}$

For the general case of equations (7)-(8), inversion must be applied tocompute A₀ and φ₀.

If multiple transverse elemental antennas are used that are located atsubstantially the same longitudinal position on the tool axis, it ispossible to form a virtual transversal antenna by combining the multipletransversal antennas. The combination may be done either by electricallyconnecting the antennas together or by adding their responses together,examples of which were discussed in reference to FIGS. 4A-D. Forinstance, if two transverse elemental antennas are separated by anazimuthal angle Δφ, then their combined response:

A=A ₁ cos(φ+φ₀)+A ₂ cos(φ+Δφ+φ₀)=B cos(φ+φ′)  (11)

is another cosine function of the tool face angle. In the above,

$\begin{matrix}{B = \left( {A_{1}^{2} + A_{2}^{2} + {2A_{1}A_{2}\; \cos \; {\Delta\varphi}}} \right)^{1/2}} & (12) \\{\varphi^{\prime} = {\tan^{- 1}\left( \frac{{A_{1}\; \sin \; \varphi_{0}} + {A_{2}\; \sin \; \left( {\varphi_{0} + {\Delta\varphi}} \right)}}{{A_{1}\; \cos \; \varphi_{0}} + {A_{2}\; \cos \; \left( {\varphi_{0} + {\Delta\varphi}} \right)}} \right)}} & (13)\end{matrix}$

Advantageously, combined antennas or signals over individual antennas orsignals may lead to better noise rejection and improved signal-to-noiseratios. And, if one of the antennas fails, the combined signal willstill be usable.

Signals from multiple transverse elemental receiving antennas may beacquired simultaneously when a transmitting antenna fires. The signalsmay also be acquired sequentially as a transmitting antenna fires,regardless of tool rotation. The tool face angle will be recorded by asensor while recording the signals. The signals are associated with thetool face measurements in computing a formation parameter of interest.When the tool rotates, measurements from two transverse (e.g., X and Y)elemental receiving antennas as a function of tool face angle willresemble each other, which provides data redundancy. Combining a largerset of measurements may be used for subsequent processing andinterpretation, while independently processing measurements from eachtransverse elemental antenna may be used for quality control purposes,among others.

Cross-component antenna arrangements (e.g., an axial transmittingantenna and a transverse elemental receiving antenna) disclosed hereinmay be used for making azimuthal resistivity measurements for detectionand resolution of an adjacent bed boundary in a formation. However,detection and resolution of adjacent bed boundaries using suchcross-component antenna arrangements may oftentimes be affected byformation resistivity anisotropy (e.g., directionally dependentformation properties). That is, formation resistivity anisotropy mayproduce an anomalous signal similar to that produced by an adjacent bedboundary. The cross-component response to an anisotropic formation maybe written as:

$\begin{matrix}{V_{zx} = {\frac{M_{T}M_{R}I}{4\pi \; L^{3}}\left\lbrack {\frac{\cos \; \theta}{\sin \; \theta}{ik}_{h}{L\left( {^{\; k_{h}L} - ^{\; k_{h}\beta \; L}} \right)}} \right\rbrack}} & (14)\end{matrix}$

Where:

$\begin{matrix}{{k_{h} = \left( {\omega\mu\sigma}_{h} \right)^{1/2}}{\beta = \left( {{\cos^{2}\; \theta} + {\frac{R_{h}}{R_{v}}\sin^{2}\; \theta}} \right)^{1/2}}} & (15)\end{matrix}$

In the above equation, M_(T) and M_(R) are the effective areas of thetransmitting and receiving antennas, respectively, I is the drivingcurrent in the transmitting antenna, and θ is the relative dip angle ofthe formation relative to the tool axis. If the resistivity anisotropyis produced by lamination of thin beds of different resistivity values,the relative dip angle θ will be 90 degrees if the wellbore (or toolaxis) is parallel to the bedding planes. V_(zx) will be nonzero as longas the relative dip angle θ is different from 0 or 90 degrees. Asdetermined from equation (14), the cross-component signal V_(zx) willremain the same if the relative dip angle changes by 180 degrees.Therefore, an axial transmitting antenna located longitudinally on oneside of the receiving antenna will produce the same response as if thetransmitting antenna is moved to the other side of the receiving antennaat a symmetrical position and driven with the same driving current.Hence, a signal response due to an anisotropic formation may be removedby subtracting the responses generated by two longitudinally symmetricaltransmitting antennas. In contrast, the responses produced at anadjacent bed boundary due to two longitudinally symmetrical transmittingantennas will have opposite signs if the axial magnetic moments of thetransmitting antennas point in the same longitudinally direction. Hence,subtracting the two responses from each other will enhance the bedboundary response.

A method of data acquisition is disclosed for suppressing certainformation parameters while amplifying others, which includes firing twotransmitting antennas at least substantially simultaneously. Currentsmay be driven simultaneously to two transmitting antennas for generatingaxial magnetic moments in opposite directions, thereby inducing avoltage signal in the wire winding of the receiving antenna related to aparameter of an adjacent formation bed boundary (and reducing orcancelling the formation resistivity anisotropy effect). Alternatively,currents may be driven simultaneously to two transmitting antennas forgenerating axial magnetic moments in the same direction, therebyinducing a voltage signal in the wire winding of the receiving antennarelated to a parameter of formation resistivity anisotropy (and reducingor cancelling the bed boundary effect).

Simultaneously driving currents to the two transmitting antennasproduces a stronger signal and greater signal-to-noise ratio (SNR) thansequentially driving currents to transmitting antennas at the same powerinput. As an example, for total data acquisition time of T, and V₀indicating the voltage signal detected by a receiving antenna for a unitdriving current in a transmitting antenna, the power consumption by thetransmitting antenna may be written as:

P=I ² R  (16)

where R is the total resistance of the antenna, i.e., the sum of theantenna wire resistance and the antenna radiation resistance. Noise inthe received signal may be assumed to be random and stacking of datawill result in reduction in noise according to:

n=cn ₀ /√{square root over (t)}  (17)

where n₀ is the noise level without any stacking, t is the acquisitiontime, and c is a proportionality constant. For sequential acquisition,the signal level is calculated by:

$\begin{matrix}{V_{1} = {V_{0}\sqrt{\frac{P}{R}}}} & (18)\end{matrix}$

Combining the two sequential measurements will result in asignal-to-noise (SNR) ratio for the combined signal calculated by:

$\begin{matrix}{{SNR}_{1} = \frac{V_{0}\sqrt{{PT}/R}}{{cn}_{0}}} & (19)\end{matrix}$

Similarly, for simultaneous acquisition, the total signal level iscalculated by:

$\begin{matrix}{V_{1} = {V_{0}\sqrt{\frac{2P}{R}}}} & (20)\end{matrix}$

The corresponding SNR is calculated by:

$\begin{matrix}{{SNR}_{2} = {\frac{V_{0}\sqrt{2{{PT}/R}}}{{cn}_{0}} = {\sqrt{2}{SNR}_{1}}}} & (21)\end{matrix}$

As shown, the SNR for simultaneous acquisition is increased by a factorof √{square root over (2)} over sequential acquisition for the sameinput power. After binning the measurements made at multiple tool faceangles into a number of sectors, the SNR for each sector will be lessthan that for the entire data combined. However, the relative gain inthe SNR for each sector with simultaneous acquisition will remain thesame as compared to sequential acquisition. In simultaneous acquisition,the two antennas preferably have the same effective cross-sectional areaand are driven with currents of the same magnitude. If they havedifferent effective cross-sectional areas, the driving currents thenmust be adjusted such that the products of the effective cross-sectionalarea and the driving current are the same.

In the above discussion, the two transmitting antennas are substantiallyequally spaced apart from the receiving antenna(s). In instances wherethe two transmitting antennas have different spacings from the receivingantenna(s), additional methods for compensating for formation anisotropyeffect are disclosed. In a first method, the two signals may bemeasured, with either sequential data acquisition or simultaneous dataacquisition, and subtracted. Subtracting the signals may work if thecoil spacing is small. As an example, coil spacing may be less than teninches or less than twenty inches. In other examples, coil spacing maybe twenty inches or greater. FIG. 7 illustrates a graph 700 showingsignal responses due to an anisotropic formation, an uncompensatedsignal response 702 and compensated signal response 704 using the firstmethod. The parameters are: Rh=1 ohmm, Rv=5 ohmm, θ=100°, L₁=40 in.,L₂=38 in., and f=2 MHz. The compensated signal is defined as:

$\begin{matrix}{V_{zx}^{Comp} = {\frac{1}{2}\left( {V_{{zx}\; 1} - V_{{zx}\; 2}} \right)}} & (22)\end{matrix}$

A coefficient of ½ is included so that after the compensation the bedboundary response remains the same (if the bed boundary is parallel tothe tool axis). As shown, the first compensation method reduces theanisotropy effect by a factor of approximately 9.1, which represents agreat reduction in the anisotropy effect.

In a second method, equation (22) is corrected by adjusting the scalingfactor L (see equation (14)) to further compensate for the formationanisotropy effect. The two individual signals may be combined as followsto produce a new compensated signal:

$\begin{matrix}{V_{zx}^{Comp} = {\frac{1}{L_{1}^{3} + L_{2}^{3}}\left( {{V_{{zx}\; 1}L_{1}^{3}} - {V_{{zx}\; 2}L_{2}^{3}}} \right)}} & (23)\end{matrix}$

As shown, equation (23) reduces to equation (22) if L₁=L₂. FIG. 8illustrates a graph 800 showing signal responses due to an anisotropicformation, an uncompensated signal response 802 and compensated signalresponse 804 using the second method according to equation (23). Thesecond compensation method reduces the anisotropy effect by a factor ofapproximately 16.3, nearly doubling that of the first compensationmethod. Equation (23) may also be implemented for simultaneous dataacquisition. To do so, the currents in the two transmitter antennas arescaled by factors of L₁ ³/(L₁ ³+L₂ ³) and L₂ ³/(L₁ ³+L₂ ³),respectively.

In a third method, the anisotropy effect is directly removed from signalmeasurements by numerically computing the anisotropy effect usingequation (14). In the equation, the two unknown parameters Rh and β maybe calculated from the propagation resistivity measurements. Therelative dip angle θ must be input from other sources, e.g., the welldeviation angle and the known formation dip angle.

An azimuthal resistivity measurement tool acquires data at multiple toolface angles, which may be regularly or irregularly distributed in thetool face domain, depending on the rotation speed of the tool. It isoften desirable that the data acquired over a certain period of time ispartitioned or “binned” into sectors. A method of data binning isdisclosed. To illustrate, it may be assumed that a total of M sectorsare formed to cover the entire tool face angle range of 0° to 360°. Forthe k-th sector φ=[φ_(k),φ_(k+1)], it may be assumed that the sectorcontains N data points, d₁, for 1<i<N, with corresponding tool faceangles φ₁. The uncertainty in the tool face angle measurement for eachdata point may be defined by a fidelity function g(φ). The fidelityfunction may be different from zero only over a finite tool face anglerange. For simplicity, the fidelity function may be assumed to be thesame for all data points, although this is not necessary. Threescenarios may occur: (1) the fidelity function associated with a datapoint is contained entirely within a sector, (2) the fidelity functionis partly contained in a sector, and (3) the fidelity function iscompletely outside a sector. Equation (24) best applies to cases wherethe data points are associated with evenly distributed tool face angles.Mathematically, this may be expressed as:

$\begin{matrix}{D_{k} = \frac{\sum\limits_{i}\; {w_{i}d_{i}}}{\sum\limits_{i}\; w_{i}}} & (24)\end{matrix}$

In the above, D_(k) is the binned data for the k-th sector and

$\begin{matrix}{w_{i} = {\int_{\varphi_{k - 1}}^{\varphi_{k}}{{g\left( {\varphi - \varphi_{i}} \right)}\ {\varphi}}}} & (25)\end{matrix}$

The selection of a fidelity function for binning data must consider thesensor response characteristics and other hardware and software factors.If the sensor accuracy follows a Gaussian distribution, then thefidelity function may reasonably be taken as the Gaussian function.Binning methods disclosed herein provide that any data points close tothe boundary between two adjacent sectors contribute to the binnedvalues of both adjacent sectors. That is, when a data point resides onthe boundary between two adjacent sectors, methods disclosed split thedata value into the two adjacent sectors. When a data point falls in onesector but is within a range of uncertainty to the sector border with anadjacent sector, the data point will be assigned to both adjacentsectors with different weights, yielding a smooth transition between thetwo sectors. For example, the range of uncertainty may be within atleast one degree of the tool face angle, or at least within threedegrees of the tool face angle, or at least within five degrees of thetool face angle, or greater.

FIG. 9 illustrates a plot 900 showing data points with associatedfidelity functions. In plot 900, four data points (1, 2, 3, and 4) areillustrated along with their respective fidelity functions g(φ). Aweighted average value is to be computed and assigned to a sectorstarting at a tool face angle φ_(k−1) and ending at the tool face angleφ_(k). Data points 1 and 4 are close to the sector lines and theirrespective fidelity function curves cross the left and right sectorlines, respectively. Data points 2 and 3 have their respective fidelityfunctions fully contained between the two sector lines. As a result,data points 1 and 4 make full contributions to the average data valueassigned to the sector, whereas data points 2 and 3 make fullcontributions. The weight for each data points is calculated fromequations (27)-(29).

FIG. 10 illustrates a flow chart showing steps of binning methodsdisclosed herein. Step (1002) indicates partitioning resistivityinformation acquired at multiple tool body angles into M number ofsectors. Step (1004) indicates defining each data point of theresistivity information by a fidelity function g(Φ). Step (1006)indicates assigning to each data point a weight for each of the M numberof sectors, wherein the weight is proportional to an integral of thefidelity function g(Φ) over the sector. Step (1008) indicates adding thedata points weighted by their respective weights for each of the Msectors.

Data points will generally be unevenly distributed in tool face anglesand should be assigned with tool-face dependent weights in computing abinned value. As an example, the data weight for the i-th data point maybe computed as:

$\begin{matrix}{u_{i} = \frac{\varphi_{i + 1} - \varphi_{i - 1}}{2\left( {\varphi_{k} - \varphi_{k - 1}} \right)}} & (26)\end{matrix}$

In using equation (26), data points falling in the k-th sector are firstscaled according to the equation:

$\begin{matrix}{d_{i}^{*} = \frac{w_{i}d_{i}}{w_{0}}} & (27)\end{matrix}$

Where:

$\begin{matrix}{w_{0} = {\int_{- \infty}^{\infty}{{g(\varphi)}\ {\varphi}}}} & (28)\end{matrix}$

The binned data value is then calculated as:

$\begin{matrix}{D_{k} = \frac{\sum\limits_{i}\; {u_{i}d_{i}^{*}}}{\sum\limits_{i}\; u_{i}}} & (29)\end{matrix}$

The claimed subject matter is not to be limited in scope by the specificembodiments described herein. Indeed, various modifications of theinvention in addition to those described herein will become apparent tothose skilled in the art from the foregoing description. Suchmodifications are intended to fall within the scope of the appendedclaims.

What is claimed is:
 1. A method of making resistivity measurements of aformation from a wellbore being drilled, the method comprising:providing a resistivity measuring tool comprising: a tool body having asensor configured to measure the angular position of the tool bodyrelative to the wellbore, at least one axial antenna including a wirewinding for generating an axial magnetic moment, and at least onetransverse antenna disposed proximate to an outer surface of the toolbody and including a wire winding for generating a transverse magneticmoment; transmitting electromagnetic energy into the formation from atleast one of the antennas, thereby inducing a voltage signal related toa formation parameter in the wire winding of a non-transmitting antenna;measuring an angular position of the tool body relative to the wellborewith the sensor; and correlating the formation parameter with themeasured angular position of the tool body.
 2. The method of claim 1,further comprising: providing a second axial antenna including a wirewinding, wherein the transverse antenna is located between the first andsecond axial antennas; and simultaneously transmitting electromagneticenergy into the formation from the first and second axial antennas,thereby inducing a voltage signal related to the formation parameter inthe wire winding of the transverse antenna.
 3. The method of claim 2,further comprising driving currents to the first and second axialantennas for generating axial magnetic moments in opposite directions,thereby inducing a voltage signal in the wire winding of the transverseantenna related to a parameter of an adjacent bed boundary.
 4. Themethod of claim 2, further comprising driving currents to the first andsecond axial antennas for generating axial magnetic moments in the samedirection, thereby inducing a voltage signal in the wire winding of thetransverse antenna related to a parameter of formation resistivityanisotropy.
 5. The method of claim 1, further comprising: partitioning acircumference of the tool body into M number of sectors; defining eachdata point of the resistivity information by a fidelity function g(Φ);assigning to each data point a weight for each of the M number ofsectors, wherein the weight is associated with an integral of thefidelity function g(Φ) over the sector; and computing an average of thedata points weighted by their respective weights for each of the Msectors.
 6. The method of claim 1, further comprising providing multipletransverse antennas disposed proximate to the outer surface of the toolbody and azimuthally-spaced around a circumference of the tool body. 7.A method of making resistivity measurements of a formation from awellbore being drilled, the method comprising: providing a resistivitymeasuring tool comprising: a tool body having a sensor configured tomeasure the angular position of the tool body relative to the wellbore;at least two axial antennas each including a wire winding for generatingan axial magnetic moment; and a transverse antenna disposed between thetwo axial antennas and including a wire winding for generating atransverse magnetic moment; substantially simultaneously driving acurrent to the wire windings of the two axial antennas for generating acurrent loop in the formation, thereby inducing a voltage signal relatedto a formation parameter in the wire winding of the transverse antennadisposed therebetween; measuring an angular position of the tool bodyrelative to the wellbore with the sensor; and correlating the formationparameter with the measured angular position of the tool body.
 8. Themethod of claim 7, further comprising driving currents in the wirewindings of the two axial antennas to generate magnetic moments inopposite axial directions, thereby inducing a voltage signal in the wirewinding of the transverse antenna disposed therebetween related to aparameter of an adjacent bed boundary.
 9. The method of claim 7, furthercomprising driving currents in the wire windings of the two axialantennas to generate magnetic moments in the same axial direction,thereby inducing a voltage signal in the wire winding of the transverseantenna disposed therebetween related to a parameter of formationresistivity anisotropy.
 10. A method of data binning comprising:partitioning a circumference of a tool face into M number of sectors;defining each data point relating to resistivity information by afidelity function g(Φ); assigning to each data point a weight for eachof the M number of sectors, wherein the weight is associated with anintegral of the fidelity function g(Φ) over the sector; and computing anaverage of the data points weighted by their respective weights for eachof the M sectors.